Traditional viral marketing problems aim at selecting a subset of seed users for one single product to maximize its awareness in social networks. However, in real scenarios, multiple products can be promoted in social networks at the same time. At the product level, the relationships among these products can be quite intertwined, e.g., competing, complementary and independent. In this paper, we will study the "interTwined Influence Maximization" (i.e., TIM) problem for one product that we target on in online social networks, where multiple other competing/complementary/independent products are being promoted simultaneously. The TIM problem is very challenging to solve due to (1) few existing models can handle the intertwined diffusion procedure of multiple products concurrently, and (2) optimal seed user selection for the target product may depend on other products' marketing strategies a lot. To address the TIM problem, a unified greedy framework TIER (interTwined Influence EstimatoR) is proposed in this paper. Extensive experiments conducted on four different types of real-world social networks demonstrate that TIER can outperform all the comparison methods with significant advantages in solving the TIM problem.